Cooperative strategies for two-evader-one-pursuer reach-avoid differential games

Abstract

A reach-avoid differential game with two evaders and one pursuer is considered in the plane which is divided into a play region and a goal region by a straight line. Two evaders, starting from the play region, aim at reaching the goal region protected by the faster pursuer who tries to capture the evaders. This game is analysed from kind and degree in analytical forms. The information structure involves that the evaders know which one is being pursued by the pursuer while the pursuer has access to the evaders' current control inputs. We are concerned with the barrier and winning regions, by which the number of evaders reaching the goal region before being captured can be determined. Cooperative strategies for two evaders are derived based on the goal priority between team goal and individual goal. An Apollonius circle based pursuit strategy is explicitly proposed. The δ-Apollonius circle is introduced to handle with the pursuit of the second-pursued evader. When two evaders are both possible to be captured, motivated by the cooperation between two prey animals against a predator, an aiding strategy is proposed such that one evader sacrifices itself to help the other's evasion. Numerical simulations are presented.